A multi-criteria optimization approach for HDR prostate brachytherapy: I. Pareto surface approximation.

High dose rate (HDR) brachytherapy planning usually involves an iterative process of refining planning objectives until a clinically acceptable plan is produced. The purpose of this two-part study is to improve current planning practice by designing a novel inverse planning algorithm based on multi-criteria optimization (MCO). In the first part, complete Pareto surfaces were approximated and studied for prostate cases. A Pareto surface approximation algorithm was implemented within the framework of Inverse Planning Simulated Annealing. The Pareto surfaces of 140 prostate cases were approximated with the proposed MCO algorithm. For each case, the Pareto surface was represented by automatically generating 300 Pareto optimal plans, and the clinically acceptable region was identified. Thus, 42 000 Pareto optimal plans were created to characterize Pareto surfaces for all the cases. In addition, the relationship between the clinically acceptable region and four anchor plans was studied. As a result, a set of polynomial regression models was extracted to rapidly predict the clinically acceptable region on the Pareto surface based on anchor plans. Pareto surfaces for HDR brachytherapy prostate cases were well characterized in this study. The proposed regression models may help define the most relevant solution phase space.